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**Adding and Subtracting Polynomials**

Section 5.4 Adding and Subtracting Polynomials

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**5.4 Lecture Guide: Adding and Subtracting Polynomials**

Objective 1: Use the terminology associated with polynomials. Monomials Polynomials Verbally A monomial is a real number, a variable, or a product of real numbers and variables with _______________ number exponents. A polynomial is a monomial or a sum of a finite number of _______________. Algebraic Examples – 5, , x, A, 5x, 7xy and are monomials. and are polynomials. is a polynomial.

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**A binomial is a polynomial containing _______________ terms.**

Trinomial Verbally A binomial is a polynomial containing _______________ terms. A trinomial is a polynomial containing _______________ terms. Algebraic Examples

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Degree of a Monomial The degree of a monomial is the sum of the _______________ for all the variables in this term. A nonzero constant is understood to have degree _______________ with exponent , but no degree is assigned to the monomial 0.

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**1. Determine whether each expression is a monomial. If the**

expression is a monomial, give its coefficient and the degree of each monomial. (a) (b) (c) (d) Monomial? Yes / No Coefficient: ______ Degree: ______

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**2. Determine whether each expression is a polynomial.**

Classify each polynomial according to the number of terms it contains. (a) (b) (c) (d) Polynomial? Yes / No Classification: ____________

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**Standard Form of a Polynomial**

A polynomial is in standard form if (1) the variables in each term are written in ____________ order and (2) the terms are arranged in ____________ powers of the first variable. Degree of a Polynomial The degree of a polynomial is the same as the degree of the term with the ____________ degree. To find this highest degree, examine each term individually---do not sum the degrees of the terms.

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**3. Write each polynomial in standard form, and give the**

degree of each polynomial. (a) Standard form: Degree:

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**3. Write each polynomial in standard form, and give the**

degree of each polynomial. (b) Standard form: Degree:

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**3. Write each polynomial in standard form, and give the**

degree of each polynomial. (c) Standard form: Degree:

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**Objective 2: Add and subtract polynomials.**

When adding or subtracting polynomials, remember to use the __________________ property to remove any grouping symbols and then add like terms. Remember that like terms have exactly the same ________ factors.

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**Identify each pair of terms as like or unlike.**

4. and 5. and

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**Determine the sum or difference and write the result in standard form.**

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**Determine the sum or difference and write the result in standard form.**

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**Determine the sum or difference and write the result in standard form.**

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**Determine the sum or difference and write the result in standard form.**

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**Determine the sum or difference and write the result in standard form.**

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**Determine the sum or difference and write the result in standard form.**

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**Determine the sum or difference and write the result in standard form.**

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**Determine the sum or difference and write the result in standard form.**

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**14. The profit in dollars made by selling x units is given**

by the polynomial Evaluate and interpret each expression. (a) Evaluate Interpret

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**14. The profit in dollars made by selling x units is given**

by the polynomial Evaluate and interpret each expression. (b) Evaluate Interpret

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**14. The profit in dollars made by selling x units is given**

by the polynomial Evaluate and interpret each expression. (c) Evaluate Interpret

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**15. Write a polynomial for the perimeter of the polygon.**

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8-1 Adding and Subtracting Polynomials. Degree of a monomial: is the sum of the exponents of its variables. The degree of a nonzero constant is 0. Zero.

8-1 Adding and Subtracting Polynomials. Degree of a monomial: is the sum of the exponents of its variables. The degree of a nonzero constant is 0. Zero.

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